We are asked to find the area of the unshaded part of the rectangle. In order to do that, we need to calculate the area of the big rectangle and then subtract from it the areas of the shaded triangle and square.
Area of the Rectangle
Let's start by recalling that the area of a rectangle is the product of its length l by the width w.
A_(rectangle)=wl
From the diagram, we know that the width of the rectangle is 120 feet and the length is 250 feet.
Let's substitute w with 120 and l with 250 into the formula and solve it for A.
The area of a triangle is half the product of the height and the corresponding base.
A_(triangle)=1/2bh
It is given on the diagram that the height of the shaded triangle is 120 feet and the length of the base is 50 feet.
Let's substitute h with 120 and b with 50 into the formula and find the area of the shaded triangle.
We conclude that the area of the shaded triangle is 3000ft^2.
Area of the Square
Let's review that the area of a square is a square of its side's length a.
A_(square)=a^2
From the diagram, we know that the length of the square's side is 100 feet.
Substituting 100 for a into the formula, we can find the area of the shaded square.
We conclude that area of the square is 10 000ft^2.
Area of the Unshaded Part
Let's start by gathering all the information we have found.
A_(rectangle)&=30 000 ft^2
A_(triangle)&=3000 ft^2
A_(square)&=10 000 ft^2
Subtracting the area of the triangle and square from the area of the rectangle, we can find the area of the unshaded part.
A=30 000-3000-10 000=17 000 ft^2
